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Paper Abstract and Keywords
Presentation 2007-05-25 15:55
Optimality and Algorithms for the Balanced Edge Cover Problem
Yuta Harada, Hirotaka Ono, Kunihiko Sadakane, Masafumi Yamashita (Kyushu Univ.) COMP2007-17
Abstract (in Japanese) (See Japanese page) 
(in English) For an undirected graph $G = (V, E)$, an edge cover is defined as a set of edges that covers all vertices of $V$. It is known that a minimum edge cover can be found in polynomial time and forms a collection of star graphs. In this paper, we consider the problem of finding a balanced edge cover where the degrees of star center vertices are balanced, which can be applied to optimize sensor network structures, for example. To this end, we formulate the problem as a minimization of the summation of strictly monotone increasing convex costs associated with degrees for covered vertices, and show that the optimality can be characterized as the non-existence of certain alternating paths. By using this characterization, we show that the optimal covers are also minimum edge covers, have the lexicographically smallest degree sequence of the covered vertices, and minimize the maximum degree of covered vertices. Based on the characterization we also present an $O(|V||E|)$ time algorithm.
Keyword (in Japanese) (See Japanese page) 
(in English) balanced edge cover / sensor network / strictly monotonic increasing convex function / / / / /  
Reference Info. IEICE Tech. Rep., vol. 107, no. 73, COMP2007-17, pp. 37-42, May 2007.
Paper # COMP2007-17 
Date of Issue 2007-05-18 (COMP) 
ISSN Print edition: ISSN 0913-5685    Online edition: ISSN 2432-6380
Copyright
and
reproduction		 All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034)
Download PDF COMP2007-17

Conference Information
Committee COMP  
Conference Date 2007-05-25 - 2007-05-25 
Place (in Japanese) (See Japanese page) 
Place (in English) Kyushu University 
Topics (in Japanese) (See Japanese page) 
Topics (in English)  
Paper Information
Registration To COMP 
Conference Code 2007-05-COMP 
Language English 
Title (in Japanese) (See Japanese page) 
Sub Title (in Japanese) (See Japanese page) 
Title (in English) Optimality and Algorithms for the Balanced Edge Cover Problem 
Sub Title (in English)  
Keyword(1) balanced edge cover  
Keyword(2) sensor network  
Keyword(3) strictly monotonic increasing convex function  
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1st Author's Name Yuta Harada  
1st Author's Affiliation Kyushu University (Kyushu Univ.)
2nd Author's Name Hirotaka Ono  
2nd Author's Affiliation Kyushu University (Kyushu Univ.)
3rd Author's Name Kunihiko Sadakane  
3rd Author's Affiliation Kyushu University (Kyushu Univ.)
4th Author's Name Masafumi Yamashita  
4th Author's Affiliation Kyushu University (Kyushu Univ.)
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Speaker Author-1 
Date Time 2007-05-25 15:55:00 
Presentation Time 35 minutes 
Registration for COMP 
Paper # COMP2007-17 
Volume (vol) vol.107 
Number (no) no.73 
Page pp.37-42 
#Pages 6 
Date of Issue 2007-05-18 (COMP) 

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